Finite Group Databasebeta

← Group #13155292

Character table — Group #13155292

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size11111111222222222222222222222222444444444444444444444444666666666666888888881212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121818181818181818181818182727272727272727363636363636363636363636
order12224444333666666666121212121212121212121212333666666666121212121212121212121212224444448888366612121212666666661212121212121212121212121212121212121212121212122424242424242424242424242424242444448888888888888888121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ511111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111111
χ91111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1ii−i−i1111-1-1-1-11111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i
χ101111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1−i−iii1111-1-1-1-11111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii11-1-1−i−iii−i−iii−i−i−i−iiiii11-1-1−i−iii−i−iii
χ111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111ii−i−i1111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-1-111ii−i−i−i−iii−i−i−i−iiiii-1-111−i−iiiii−i−i
χ121111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111−i−iii1111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii-1-111−i−iiiii−i−iiiii−i−i−i−i-1-111ii−i−i−i−iii
χ131111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-11111ii−i−iii−i−iiiii−i−i−i−i-1-111−i−iiiii−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii
χ141111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−iii1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-11111−i−iii−i−iii−i−i−i−iiiii-1-111ii−i−i−i−iiiiiii−i−i−i−i-1-111−i−iiiii−i−i
χ151111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111ii−i−iii−i−iiiii−i−i−i−i11-1-1−i−iii−i−iiiiiii−i−i−i−i11-1-1−i−iii−i−iii
χ161111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−iii1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111−i−iii−i−iii−i−i−i−iiiii11-1-1ii−i−iii−i−i−i−i−i−iiiii11-1-1ii−i−iii−i−i
χ1711-1-111-1-1111-1-11-1-111-1-111-1-1-1-111-1-111111-1-1-1-111-1-1111-1-1-1-111-1-1111-11-1i−ii−i1-11-11-1-1111-1-111-1-111-1-1i−ii−i11-1-1i−ii−iii−i−iii−i−i11-1-11-11-11-11-111-1-111-1-1i−ii−i1-11-1i−ii−iii−i−iii−i−ii−ii−ii−ii−i1-11-1
χ1811-1-111-1-1111-1-11-1-111-1-111-1-1-1-111-1-111111-1-1-1-111-1-1111-1-1-1-111-1-1111-11-1i−ii−i-11-111-1-1111-1-111-1-111-1-1i−ii−i11-1-1i−ii−iii−i−iii−i−i11-1-1-11-11-11-11-1-111-1-111i−ii−i-11-11−ii−ii−i−iii−i−iiii−ii−i−ii−ii-11-11
χ1911-1-111-1-1111-1-11-1-111-1-111-1-1-1-111-1-111111-1-1-1-111-1-1111-1-1-1-111-1-1111-11-1−ii−ii1-11-11-1-1111-1-111-1-111-1-1−ii−ii11-1-1−ii−ii−i−iii−i−iii11-1-11-11-11-11-111-1-111-1-1−ii−ii1-11-1−ii−ii−i−iii−i−iii−ii−ii−ii−ii1-11-1
χ2011-1-111-1-1111-1-11-1-111-1-111-1-1-1-111-1-111111-1-1-1-111-1-1111-1-1-1-111-1-1111-11-1−ii−ii-11-111-1-1111-1-111-1-111-1-1−ii−ii11-1-1−ii−ii−i−iii−i−iii11-1-1-11-11-11-11-1-111-1-111−ii−ii-11-11i−ii−iii−i−iii−i−i−ii−iii−ii−i-11-11
χ2111-1-111-1-1111-1-11-1-111-1-111-1-1-1-111-1-111111-1-1-1-111-1-1111-1-1-1-111-1-111-11-11i−ii−i1-11-11-1-1111-1-1-1-111-1-111i−ii−i-1-111i−ii−iii−i−iii−i−i-1-1111-11-11-11-111-1-111-1-1−ii−ii-11-11i−ii−i−i−iii−i−iii−ii−iii−ii−i-11-11
χ2211-1-111-1-1111-1-11-1-111-1-111-1-1-1-111-1-111111-1-1-1-111-1-1111-1-1-1-111-1-111-11-11i−ii−i-11-111-1-1111-1-1-1-111-1-111i−ii−i-1-111i−ii−iii−i−iii−i−i-1-111-11-11-11-11-1-111-1-111−ii−ii1-11-1−ii−iiii−i−iii−i−i−ii−ii−ii−ii1-11-1
χ2311-1-111-1-1111-1-11-1-111-1-111-1-1-1-111-1-111111-1-1-1-111-1-1111-1-1-1-111-1-111-11-11−ii−ii1-11-11-1-1111-1-1-1-111-1-111−ii−ii-1-111−ii−ii−i−iii−i−iii-1-1111-11-11-11-111-1-111-1-1i−ii−i-11-11−ii−iiii−i−iii−i−ii−ii−i−ii−ii-11-11
χ2411-1-111-1-1111-1-11-1-111-1-111-1-1-1-111-1-111111-1-1-1-111-1-1111-1-1-1-111-1-111-11-11−ii−ii-11-111-1-1111-1-1-1-111-1-111−ii−ii-1-111−ii−ii−i−iii−i−iii-1-111-11-11-11-11-1-111-1-111i−ii−i1-11-1i−ii−i−i−iii−i−iiii−ii−ii−ii−i1-11-1
χ2511-1-1-1-111111-1-11-1-111-1-1-1-11111-1-111-1-1111-1-1-1-111-1-11-1-11111-1-111-1-11-1-11i−i−iii−i−ii1-1-11-1-11111-1-111-1-1i−i−ii-1-111i−i−iiii−i−i−i−iii-1-111i−i−iii−i−iiii−i−i−i−iiii−i−iii−i−ii-111-1-1-11111-1-1i−i−ii-111-1i−i−ii
χ2611-1-1-1-111111-1-11-1-111-1-1-1-11111-1-111-1-1111-1-1-1-111-1-11-1-11111-1-111-1-11-1-11i−i−ii−iii−i1-1-11-1-11111-1-111-1-1i−i−ii-1-111i−i−iiii−i−i−i−iii-1-111−iii−i−iii−i−i−iiiii−i−ii−i−ii−iii−i1-1-1111-1-1-1-111i−i−ii1-1-11−iii−i
χ2711-1-1-1-111111-1-11-1-111-1-1-1-11111-1-111-1-1111-1-1-1-111-1-11-1-11111-1-111-1-11-1-11−iii−ii−i−ii1-1-11-1-11111-1-111-1-1−iii−i-1-111−iii−i−i−iiiii−i−i-1-111i−i−iii−i−iiii−i−i−i−iii−iii−ii−i−ii1-1-1111-1-1-1-111−iii−i1-1-11i−i−ii
χ2811-1-1-1-111111-1-11-1-111-1-1-1-11111-1-111-1-1111-1-1-1-111-1-11-1-11111-1-111-1-11-1-11−iii−i−iii−i1-1-11-1-11111-1-111-1-1−iii−i-1-111−iii−i−i−iiiii−i−i-1-111−iii−i−iii−i−i−iiiii−i−i−iii−i−iii−i-111-1-1-11111-1-1−iii−i-111-1−iii−i
χ2911-1-1-1-111111-1-11-1-111-1-1-1-11111-1-111-1-1111-1-1-1-111-1-11-1-11111-1-111-1-1-111-1i−i−iii−i−ii1-1-11-1-111-1-111-1-111i−i−ii11-1-1i−i−iiii−i−i−i−iii11-1-1i−i−iii−i−iiii−i−i−i−iii−iii−i−iii−i-111-111-1-1-1-111−iii−i-111-1−iii−i
χ3011-1-1-1-111111-1-11-1-111-1-1-1-11111-1-111-1-1111-1-1-1-111-1-11-1-11111-1-111-1-1-111-1i−i−ii−iii−i1-1-11-1-111-1-111-1-111i−i−ii11-1-1i−i−iiii−i−i−i−iii11-1-1−iii−i−iii−i−i−iiiii−i−i−iii−ii−i−ii1-1-11-1-11111-1-1−iii−i1-1-11i−i−ii
χ3111-1-1-1-111111-1-11-1-111-1-1-1-11111-1-111-1-1111-1-1-1-111-1-11-1-11111-1-111-1-1-111-1−iii−ii−i−ii1-1-11-1-111-1-111-1-111−iii−i11-1-1−iii−i−i−iiiii−i−i11-1-1i−i−iii−i−iiii−i−i−i−iiii−i−ii−iii−i1-1-11-1-11111-1-1i−i−ii1-1-11−iii−i
χ3211-1-1-1-111111-1-11-1-111-1-1-1-11111-1-111-1-1111-1-1-1-111-1-11-1-11111-1-111-1-1-111-1−iii−i−iii−i1-1-11-1-111-1-111-1-111−iii−i11-1-1−iii−i−i−iiiii−i−i11-1-1−iii−i−iii−i−i−iiiii−i−ii−i−iii−i−ii-111-111-1-1-1-111i−i−ii-111-1i−i−ii
χ332222222222-1222222-1-1-1-1-122-1-12222222-1-122-1-12-1-1-1-1-1-122-1-1-1-1-1-122222222220000-1-1-1-1-1-1-1-12-12-1-1-1-1-122222-12-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022220000000000000000-1-1-1-100000000
χ342222222222-1222222-1-1-1-1-122-1-12222222-1-122-1-12-1-1-1-1-1-122-1-1-1-1-1-1222222-2-2-2-20000-1-1-1-1-1-1-1-12-12-1-1-1-1-1-2-2-2-22-12-1111111111111-1-1-1-10000000000000000-2-2-2-20000000000000000111100000000
χ352222222222-1222222-1-1-1-1-122-1-12222222-1-122-1-12-1-1-1-1-1-122-1-1-1-1-1-122-2-2-2-222220000-1-1-1-1-1-1-1-1-21-2111112222-21-21-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000-2-2-2-20000000000000000111100000000
χ362222222222-1222222-1-1-1-1-122-1-12222222-1-122-1-12-1-1-1-1-1-122-1-1-1-1-1-122-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-1-21-211111-2-2-2-2-21-211111111111111111000000000000000022220000000000000000-1-1-1-100000000
χ37222222222-12-1-1222-122222-1-1222222-1-1-12-1-1-1-1-1-1222-122-1-122-1-1-1-1-1-1222200002222-1-1-1-1-1-1-1-1-12-12-1-1-1-10000-12-12000000000000-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000222200000000000000000000-1-1-1-1
χ38222222222-12-1-1222-122222-1-1222222-1-1-12-1-1-1-1-1-1222-122-1-122-1-1-1-1-1-122220000-2-2-2-2-1-1-1-1-1-1-1-1-12-12-1-1-1-10000-12-12000000000000-1-1-1-1-2-2-2-21111111111110000-2-2-2-2000000000000000000001111
χ39222222222-12-1-1222-122222-1-1222222-1-1-12-1-1-1-1-1-1222-122-1-122-1-1-1-1-1-1-2-2-2-200002222-1-1-1-1-1-1-1-11-21-2111100001-21-200000000000011112222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000000000000000001111
χ40222222222-12-1-1222-122222-1-1222222-1-1-12-1-1-1-1-1-1222-122-1-122-1-1-1-1-1-1-2-2-2-20000-2-2-2-2-1-1-1-1-1-1-1-11-21-2111100001-21-20000000000001111-2-2-2-21111111111110000222200000000000000000000-1-1-1-1
χ4122222222-12222-1-1-12222222222-1-1-1-122-1-12-1-122-1-1-1-12-1-1-1-1-1-12222-1-1000022222222-1-1-1-1-1-1-1-100000000-1-1-1-100002222-1-1-1-1-1-1-1-10000-1-1-1-12222-1-1-1-1-1-1-1-1000000002222000000000000-1-1-1-10000
χ4222222222-12222-1-1-12222222222-1-1-1-122-1-12-1-122-1-1-1-12-1-1-1-1-1-12222-1-100002222-2-2-2-2-1-1-1-1-1-1-1-100000000-1-1-1-100002222-1-1-1-1-1-1-1-100001111-2-2-2-21111111100000000-2-2-2-200000000000011110000
χ4322222222-12222-1-1-12222222222-1-1-1-122-1-12-1-122-1-1-1-12-1-1-1-1-1-12222-1-10000-2-2-2-22222-1-1-1-1-1-1-1-10000000011110000-2-2-2-2111111110000-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2-2-200000000000011110000
χ4422222222-12222-1-1-12222222222-1-1-1-122-1-12-1-122-1-1-1-12-1-1-1-1-1-12222-1-10000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000000011110000-2-2-2-21111111100001111-2-2-2-211111111000000002222000000000000-1-1-1-10000
χ452222-2-2-2-222-1222222-1-1-111-2-211-2-2-2-2-2-22-1-122-1-12-1-1-1-111-2-2111111-2-222-2-222-2-20000-1-1-1-111112-12-1-1-1-1-122-2-2-21-21-1-111-1-1-1-111111111000000000000000022-2-20000000000000000-1-11100000000
χ462222-2-2-2-222-1222222-1-1-111-2-211-2-2-2-2-2-22-1-122-1-12-1-1-1-111-2-2111111-2-222-2-2-2-2220000-1-1-1-111112-12-1-1-1-1-1-2-222-21-2111-1-11111-1-1-1-111110000000000000000-2-222000000000000000011-1-100000000
χ472222-2-2-2-222-1222222-1-1-111-2-211-2-2-2-2-2-22-1-122-1-12-1-1-1-111-2-2111111-2-2-2-22222-2-20000-1-1-1-11111-21-21111122-2-22-12-1-1-111-1-1-1-11111-1-1-1-10000000000000000-2-222000000000000000011-1-100000000
χ482222-2-2-2-222-1222222-1-1-111-2-211-2-2-2-2-2-22-1-122-1-12-1-1-1-111-2-2111111-2-2-2-222-2-2220000-1-1-1-11111-21-211111-2-2222-12-111-1-11111-1-1-1-1-1-1-1-1000000000000000022-2-20000000000000000-1-11100000000
χ492222-2-2-2-22-12-1-1222-1222-2-211-2-2-2-2-2-211-12-1-1-1-1-1-1222-1-2-211-2-211111122-2-200002i2i−2i−2i-1-1-1-11111-12-12-1-1-1-100001-21-200000000000011112i2i−2i−2i−i−iii−i−i−i−iiiii00002i2i−2i−2i00000000000000000000−i−iii
χ502222-2-2-2-22-12-1-1222-1222-2-211-2-2-2-2-2-211-12-1-1-1-1-1-1222-1-2-211-2-211111122-2-20000−2i−2i2i2i-1-1-1-11111-12-12-1-1-1-100001-21-20000000000001111−2i−2i2i2iii−i−iiiii−i−i−i−i0000−2i−2i2i2i00000000000000000000ii−i−i
χ512222-2-2-2-22-12-1-1222-1222-2-211-2-2-2-2-2-211-12-1-1-1-1-1-1222-1-2-211-2-2111111-2-22200002i2i−2i−2i-1-1-1-111111-21-211110000-12-12000000000000-1-1-1-12i2i−2i−2i−i−iii−i−i−i−iiiii0000−2i−2i2i2i00000000000000000000ii−i−i
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.